Question

A lady gives a dinner party to six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is:

• A. 112
• B. 140
• C. 164
• D. None of these

Answer 1

Answer: (B)

140

Answer 2

Total friends 10, number of friends to be invited = 6.

Case I: If both of them are not present in party.

Number of ways of inviting them = $8C_{6} = 28$.

Case II: If one of them is present in the party, then number of ways of inviting them

= $2C_{1}x^{8}C_{5} = 112$.

Total = 140